146C

Office hours: Friday at 2-3pm in Skye 259

Email: nchie005@ucr.edu

Please feel free to contact me with any questions via email. If the office hours times do not work for you and you would like to meet, don't hesitate to reach out!

*All material is supplementary and is not to be used as the primary material for the course. 

Color coding of notes:

• Black - Theorems, Lemmas, Context, Writing in General

• Grey - Reserved for proofs 

• Green - Definitions

• Red - Examples, Exercises

• Blue - Remarks, Clarification, Justification

Week 0 - Notes + review worksheet.

Key takeaways:

1. Review of multivariable, such as partial derivatives, gradients, divergence.

2. Differential operators act on function spaces. Examples could be partial derivatives, nabla, divergence, laplacian operator.

3. How to identify a PDE and the order.

Week 1 - Review of transport and wave equation.

Key takeaways:

1. Can identify if the PDE is of the form of a transport equation or wave equation.

2. Understands how to solve constant coefficient and variable coefficient transport equation.

3. Can solve homogeneous wave equation using d'Alembert's formula.

Week 2 - Review of wave equation with Neumann and Dirichlet boundary
Some minor typos as (t,x) should be written as (x,t) in some places.

Key takeaways:

1. Can identify if the wave equation has Neumann or Dirichlet boundary.

2. Can solve Neumann IVP problems.

3. Can solve Dirichlet IVP problems.

Week 3 - Review of wave equation, heat equation unbounded , and heat equation bounded.

Key takeaways: 

1. Can use separation of variables to find the solution of the wave equation.

2. Can use Fourier transformations to find solution to the unbounded heat equation.

3. Can use separation of variables to find the solutions of the bounded heat equation.

4. If given an unbounded heat equation can use the convolution formula from (2) to solve.

5. If given a bounded heat equation can use the formula determined from (3) to solve.

Week 4 - Review of uniqueness of solutions and Fourier transforms.

Week 5 - No office hours on Friday, as office hours held on Monday for exam review.